Simplifying Multiple Sums in Difference Fields
TLDR
This survey article presents difference field algorithms for symbolic summation that can be solved completely automatically for large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics).Abstract:
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package Sigma by discovering and proving new harmonic number identities extending those from Paule and Schneider, 2003. In addition, the newly developed package EvaluateMultiSums is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.read more
Citations
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Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra
Jakob Ablinger,A. Behring,Johannes Blümlein,A. De Freitas,A. von Manteuffel,Carsten Schneider +5 more
TL;DR: This work relies on generalized hypergeometric functions and Mellin–Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist–Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations.
Journal ArticleDOI
The 3-loop pure singlet heavy flavor contributions to the structure function F2(x,Q2) and the anomalous dimension
Jakob Ablinger,A. Behring,Johannes Blümlein,A. De Freitas,A. von Manteuffel,Carsten Schneider +5 more
TL;DR: In this article, the pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function F2(x,Q 2 ) and the corresponding transition matrix element A (3),PS Qq in the variable flavor number scheme are computed.
Journal ArticleDOI
The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function F2(x,Q2) and transversity
Jakob Ablinger,A. Behring,Johannes Blümlein,A. De Freitas,A. Hasselhuhn,A. von Manteuffel,M. Round,Carsten Schneider,F. Wißbrock +8 more
TL;DR: In this paper, the massive flavor non-singlet Wilson coefficient for heavy flavor contributions to the structure function F2(x,Q 2 ) in the asymptotic region Q 2 ≫ m 2 and the associated operator matrix element A (3),NS qq,Q (N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N.
Journal ArticleDOI
Iterated binomial sums and their associated iterated integrals
TL;DR: In this article, the authors consider finite iterated generalized harmonic sums weighted by the binomial 2kk in numerators and denominators, and develop algorithms to obtain the Mellin representations of these sums in a systematic way.
Journal ArticleDOI
The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: Potential contributions
TL;DR: In this paper, the potential contributions of the motion of binary mass systems in gravity to the fifth post-Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization were calculated.
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